Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Vector Representation of Complex Numbers

Vector Representation of Complex Numbers

Complex numbers, represented in Cartesian coordinates, can also be visualized as vectors. These vectors can be expressed in polar form, emphasizing their magnitude and angle. When a complex number is input into a function, the output is another complex number, highlighting the function's zero point from which the vector representation can originate.
Consider a function defined as the product of the complex factors in the numerator divided by the product of the complex factors in the denominator.

Vector Algebra: Method of Components

Vector Algebra: Method of Components

It is cumbersome to find the magnitudes of vectors using the parallelogram rule or using the graphical method to perform mathematical operations like addition, subtraction, and multiplication. There are two ways to circumvent this algebraic complexity. One way is to draw the vectors to scale, as in navigation, and read approximate vector lengths and angles (directions) from the graphs. The other way is to use the method of components.
In many applications, the magnitudes and directions of...

Upsampling

Upsampling

Managing signal sampling rates is essential in digital signal processing to maintain signal integrity. A decimated signal, characterized by a reduced frequency range due to its lower sampling rate, can be upsampled by inserting zeros between each sample. This upsampling process expands the original spectrum and introduces repeated spectral replicas at intervals dictated by the new Nyquist frequency. To refine this zero-inserted sequence, it is passed through a lowpass filter with a cutoff...

Downsampling

Downsampling

When considering a sampled sequence with zero values between sampling instants, one can replace it by taking every N-th value of the sequence. At these integer multiples of N, the original and sampled sequences coincide. This process, known as decimation, involves extracting every N-th sample from a sequence, thereby creating a more efficient sequence.
The Fourier transform of the decimated sequence reveals a combination of scaled and shifted versions of the original spectrum. This...

Vectors

Vectors

Vectors are mathematical entities characterized by both magnitude and direction. Unlike scalars, which are defined solely by magnitude, vectors represent quantities like displacement, velocity, and force, where direction is essential. Vectors are graphically represented as directed line segments, extending from an initial point to a terminal point, denoted with bold letters or arrows placed above the symbol. Two vectors are deemed equal if they share identical magnitudes and directions,...

Conservative Vector Fields

Conservative Vector Fields

A conservative vector field describes a force or field in which the work done between two points depends only on the initial and final positions. For a ball moving in Earth’s gravitational field, gravity performs work determined by the difference in height, regardless of whether the ball moves vertically or follows a curved trajectory.A vector field is conservative if it can be expressed as the gradient of a scalar potential function, f. In two dimensions, this is written...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by

Same author

Image compression based on fuzzy algorithms for learning vector quantization and wavelet image decomposition.

IEEE transactions on image processing : a publication of the IEEE Signal Processing Society·2008

Same author

Competitive neural trees for pattern classification.

IEEE transactions on neural networks·2008

Same author

Reformulated radial basis neural networks trained by gradient descent.

IEEE transactions on neural networks·2008

Same author

An axiomatic approach to soft learning vector quantization and clustering.

IEEE transactions on neural networks·2008

Same author

Soft learning vector quantization and clustering algorithms based on ordered weighted aggregation operators.

IEEE transactions on neural networks·2008

Same author

Soft learning vector quantization and clustering algorithms based on non-Euclidean norms: multinorm algorithms.

IEEE transactions on neural networks·2008

Search research articles

Related Experiment Videos

Fuzzy vector quantization algorithms and their application in image compression.

N B Karayiannis¹, P I Pai

¹Dept. of Electr. Eng., Houston Univ., TX.

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society

|January 1, 1995

Summary

This study introduces fuzzy vector quantization algorithms that balance high-quality codebook design with the efficiency of the k-means algorithm. These novel methods improve clustering by allowing fuzzy assignments, enhancing image compression performance.

Related Experiment Videos

Area of Science:

Computer Science
Signal Processing
Machine Learning

Background:

Vector quantization (VQ) is crucial for data compression.
Sophisticated VQ methods offer high quality but are computationally intensive.
The k-means algorithm is fast and simple but may yield suboptimal codebooks.

Purpose of the Study:

To develop fuzzy vector quantization (FVQ) algorithms.
To achieve high-quality VQ comparable to complex methods.
To retain the speed and simplicity of the k-means algorithm.

Main Methods:

Formulating clustering uncertainty by assigning training vectors to multiple clusters.
Implementing an iterative codebook design process with fuzzy assignments.
Proposing a strategy for transitioning from fuzzy to crisp vector assignments.
Applying the algorithms to image compression for evaluation.

Main Results:

The developed fuzzy vector quantization algorithms achieve high-quality codebook design.
The proposed transition strategy reduces codebook dependence on initial random selection.
The algorithms demonstrate computational efficiency in image compression tasks.
Performance is comparable to existing sophisticated VQ techniques.

Conclusions:

Fuzzy vector quantization offers a promising approach for efficient and high-quality data compression.
The developed algorithms provide a practical alternative to computationally demanding VQ methods.
The fuzzy-to-crisp transition strategy enhances codebook robustness and reliability.